Big-bang nucleosynthesis enters the precision era David N. Schramm† and Michael S. Turner Departments of Physics and of Astronomy & Astrophysics, Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637-1433 and NASA/Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510-0500 The last parameter of big-bang nucleosynthesis, the density of ordinary matter (baryons), is being pinned down by measurements of the deuterium abundance in high-redshift hydrogen clouds. When it is, the primeval abundances of the light elements D, 3He, 7Li, and 4He will be fixed. The first three will then become ‘‘tracers’’ in the study of Galactic and stellar chemical evolution. A precision determination of the 4He abundance will allow an important consistency test of big-bang nucleosynthesis and will sharpen nucleosynthesis as a probe of fundamental physics, e.g., the bound to the number of light neutrino species. An independent consistency test is on the horizon: a high-precision determination of the baryon density from measurements of the fluctuations of the cosmic background radiation temperature. [S0034-6861(98)01001-0] CONTENTS g Counts the total number of spin states * of all relativistic particle species. During Glossary and List of Symbols 303 BBN, g 510.75 for the standard sce- * I. From Gamow to Keck 304 nario. See Appendix for more details. II. Keck: The Great Leap Forward 306 Hot dark Dark matter particles that move very III. The Baryon Density and its Cosmic Implications 307 matter fast (e.g., neutrinos with mass in the IV. Nuclear Cosmology Clarifies Galactic Chemistry 309 V. Helium-4: Loose End or Consistency Check? 310 range of 1 eV to 30 eV). 4 VI. A New Test of the Standard Theory 311 H II region Region of hot (T@10 K), ionized gas VII. Probing Fundamental Physics with New Precision 312 (mostly hydrogen and helium). H II re- VIII. Concluding Remarks 313 gions are common within our own gal- Acknowledments 313 axy and other galaxies. Appendix: The Physics of Big-Bang Nucleosynthesis 313 H0 Present value of the expansion rate (or 1. The ingredients 313 Hubble constant). The expansion rate 2. BBN 1-2-3 314 ˙ a. Weak-interaction freezeout 315 H[R/R, where R(t) is the cosmic b. End of nuclear statistical equilibrium scale factor. (kT.0.5 MeV) 315 Lyman-a A cloud of gas (mostly hydrogen) c. BBN (kT.0.07 MeV) 315 (Ly-a) present in the early universe that is 3. Variations on a theme 316 cloud ‘‘seen’’ by its absorption of light (in the 4. Neutrino counting 316 Lyman series) from even more distant References 316 quasars. The Lyman series begins with Ly-a at 1216 Å, continuing to the con- GLOSSARY AND LIST OF SYMBOLS tinuum limit at 912 Å. BBN Big-bang nucleosynthesis, the sequence MACHO Acronym for massive astrophysical of nuclear reactions that led to the syn- compact halo object. Refers generically thesis of the light elements D, 3He, to stars too faint to be seen (of any 4He, and 7Li between 0.01 sec and 200 mass) that might be the constituents of sec after the bang. the baryonic dark matter, e.g., white CBR The cosmic background radiation is the dwarfs, neutron stars, black holes, microwave echo of the big bang. It is brown dwarfs, or Jupiters. MACHOs blackbody radiation to a precision of can be detected by their gravitational 0.005% and has a temperature 2.7277 lensing of bright stars. K 6 0.002 K. Nn The number of neutrino species with Chemical The change in chemical composition of mass much less than 1 MeV. In the evolution (ordinary) matter due to the nuclear standard model of particle physics all transformations that take place in stars three neutrino species are massless and and elsewhere. Nn53. Sometimes Nn is used to quan- Cold dark Dark matter particles that move very tify the energy density in relativistic matter slowly (e.g., axions, neutralinos, or particles (other than photons and black holes). electron-positron pairs) at the time of BBN: g 55.511.75N . * n h The ratio of nucleons (baryons) to pho- †Deceased. tons (in the cosmic background radia- Reviews of Modern Physics, Vol. 70, No. 1, January 1998 0034-6861/98/70(1)/303(16)/$18.20 © 1998 The American Physical Society 303 304 D. N. Schramm and M. S. Turner: Big-bang nucleosynthesis tion), whose value is around 5310210, the three, big-bang nucleosynthesis probes the Universe and whose inverse is, up to a numerical to the earliest times, from a fraction of a second to hun- factor, the specific entropy per nucleon. dreds of seconds. Since BBN involves events that oc- The fraction of critical density contrib- curred at temperatures of order 1 MeV, it naturally 2 7 uted by baryons is VBh 53.64310 h. played a key role in forging the connection between cos- Nonbaryonic Measurements of the total matter den- mology and nuclear and particle physics that has blos- dark sity in the Universe exceed the BBN somed during the past fifteen years (see, for example, matter upper limit to that contributed by ordi- Kolb and Turner, 1990). nary matter (baryons), indicating the It is the basic consistency of the predictions for the presence of another form of matter abundances of the four light elements D, 3He, 4He, and (nonbaryonic). Possibilities for the non- 7Li with their measured abundances (which span more baryonic dark matter include elemen- than nine orders of magnitude) that has moved BBN to tary particles remaining from the earli- the cosmological centerstage. In its success, BBN has led est moments (e.g., axions, neutralinos, to the most accurate determination of the mass density or massive neutrinos) and primordial of ordinary matter. black holes (formed before the epoch of Currenly, there is great excitement because we are on BBN). the verge of determining the baryon density to a preci- Peculiar Motion of a galaxy or other object over sion of 20%, and ultimately to 5% or better, from mea- velocity and above that due to the expansion of surements of the primeval deuterium abundance. When the universe. More precisely, velocity this occurs, BBN will enter a qualitatively new phase, an with respect to the cosmic rest frame. era of high precision. The consequences for cosmology Peculiar velocities arise due to the inho- are obvious: an accurate determination of the average mogeneous distribution of matter and density of ordinary matter in the Universe and a completion of the BBN story. The implications for as- can be used to determine the mean trophysics are just as important: fixing the baryon den- matter density. sity fixes the primeval abundances of the light elements T-Tauri phase An unstable phase that stars like our and allows them to be used as tracers in the study of the sun go through just before they settle chemical evolution of the Galaxy and aspects of stellar down to the main-sequence (hydrogen evolution. Lastly, important limits to particle properties, burning) phase. such as the limit to the number of light neutrino species, YP The mass fraction of baryons converted 4 can be further sharpened. to He during BBN. The BBN story (see, for example, Kragh, 1996) begins 0 6 Z boson Together with the W bosons, the car- with Gamow and his collaborators, Alpher and Herman, 0 riers of the weak force. The Z medi- who viewed the early Universe as a nuclear furnace that ates the neutral-current interaction and could ‘‘cook the periodic table.’’ Their speculations, has a mass of 91.18760.007 GeV. while not correct about the details of nucleosynthesis, Vi The fraction of the critical mass density led to the prediction of the microwave echo of the big contributed by species i; e.g., baryons bang, the cosmic background radiation. Key refinements (i5B) or nonrelativistic matter include those made by Hayashi, who recognized the role (i5M), which includes baryons and of neutron-proton equilibration (see Appendix), and by cold dark matter. Turkevich and Fermi, who pointed out that lack of VTOT The fraction of critical density contrib- stable nuclei of mass 5 and 8 precludes nucleosynthesis uted by all forms of matter and energy. beyond the lightest elements. The framework for the A universe with VTOT<1 has negatively calculations themselves dates back to the work of Al- curved spatial hypersurfaces, expands pher, Follin, and Herman and of Taylor and Hoyle, pre- forever, and is said to be open; a uni- ceding the discovery of the 3K background, of Peebles and of Wagoner, Fowler, and Hoyle, immediately fol- verse with VTOT=1 has flat spatial hy- persurfaces, expands forever, and is lowing the discovery, and the more recent work of our group of collaborators (Yang et al., 1984; Walker et al., open; and a universe with VTOT>1 has positively curved spatial hypersurfaces, 1991; Smith et al., 1993; Copi et al., 1995a, 1995b, 1995c) eventually recollapses, has finite vol- and of other groups around the world (Matzner and ume, and is said to be closed. Rothman, 1982; Kurki-Sunio et al., 1990; Pagel, 1991; Sato and Terasawa, 1991; Malaney and Mathews, 1993; Audouze, 1995; Hata et al., 1995; Krauss and Kernan, I. FROM GAMOW TO KECK 1995; Fuller and Cardall, 1996; Kernan and Sarkar, 1996). Over the last two decades big-bang nucleosynthesis The basic calculation, a nuclear reaction network in (BBN) has emerged as one of the cornerstones of the an expanding box, has changed very little. The most up big bang, joining the Hubble expansion and the cosmic to date predictions are shown in Fig. 1, and the physics microwave background radiation (CBR) in this role.